This paper presents a 2-D localization system based on phase-of-arrival evaluation of passive ultrahigh frequency (UHF) radio frequency identification (RFID) transponders. To handle the ambiguity caused by phase evaluation, several tags are arranged to form a uniform linear array. A multiple input multiple output system, where sequentially each frontend is configured to work as transmitter, while the remaining frontends serve as receivers, is used to enable position estimation. For proof of concept, a local position measurement system demonstrator was built comprising conventional passive EPCglobal Class-1 Gen-2 UHF RFID tags, one commercial off-the-shelf RFID reader, several transceiver frontends, baseband hardware, and signal processing. Measurements were carried out in an indoor office environment, where the (3.5~{rm m} times 2.5) m measurement zone was surrounded by drywalls and concrete floor and ceiling, and the experimental results showed robust and accurate localization with a root-mean-square deviation of 0.011 m and a maximum error of 0.032 m. These experimental results were confirmed by simulations, which were performed to determine the limits of the system accuracy.